Subgroups — C₂×#27163848 #38770642

Order 25472.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263891	C₂	1	2	yes	maximal
2	#27163848	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₁₉₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#15691870	—	2	2	no	—
5	#20263891	—	2	2	no	—
6	#20263891	C₂²	1	4	yes	—
7	C₂²×C₈×C₁₉₉	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₁₉₉	C₄	1	2	yes	—
9	C₂×C₁₆×C₁₉₉	C₄	1	2	yes	—
10	C₂×C₁₆×C₁₉₉	C₂²	1	2	yes	—
11	#15691870	—	2	4	no	—
12	#15691870	—	4	2	no	—
13	C₂×C₁₉₉⋊C₈	—	4	2	no	—
14	C₂²×C₄×C₁₉₉	D₄	1	1	yes	characteristic
15	C₂×C₈×C₁₉₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₉₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉₉	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉₉	Q₈	1	1	yes	characteristic
19	C₂×C₈×C₁₉₉	Q₈	1	1	yes	characteristic
20	C₂×C₈×C₁₉₉	C₂³	1	1	yes	characteristic
21	C₁₆×C₁₉₉	C₂×C₄	1	4	yes	—
22	C₁₉₉⋊C₈	—	4	4	no	—
23	C₂³×C₁₉₉	Q₁₆	1	1	yes	characteristic
24	C₂×C₄×C₁₉₉	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₉₉	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₉₉	D₈	1	1	yes	characteristic
27	C₂×C₄×C₁₉₉	D₈	1	1	yes	characteristic
28	C₂×C₄×C₁₉₉	Q₁₆	1	1	yes	characteristic
29	C₂×C₄×C₁₉₉	C₂×D₄	1	1	yes	characteristic
30	C₈×C₁₉₉	C₄⋊C₄	1	1	yes	characteristic
31	C₈×C₁₉₉	C₄⋊C₄	1	1	yes	characteristic
32	C₈×C₁₉₉	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₁₉₉	C₂×Q₈	1	1	yes	characteristic
34	C₂²×C₁₉₉	—	2	2	no	—
35	C₂²×C₁₉₉	#107	1	1	yes	characteristic
36	C₂²×C₁₉₉	#107	1	1	yes	characteristic
37	C₂²×C₁₉₉	C₂×Q₁₆	1	1	yes	characteristic
38	C₄×C₁₉₉	#107	1	1	yes	characteristic
39	C₄×C₁₉₉	#107	1	1	yes	characteristic
40	C₄×C₁₉₉	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₄×C₁₉₉	C₂×D₈	1	1	yes	characteristic
42	C₂×C₁₉₉	—	2	1	no	—
43	C₂×C₁₉₉	—	2	1	no	—
44	C₂×C₁₉₉	#368	1	2	yes	complemented
45	C₂×C₁₉₉	C₂×#107	1	1	yes	characteristic
46	C₁₉₉	C₂×#368	1	1	yes	characteristic, complemented, Sylow
47	C₂×#368	—	199	1	no	maximal, Sylow
48	C₂²×C₁₆	D₁₉₉	1	1	yes	characteristic
49	C₂×#108	—	199	2	no	—
50	#368	—	199	4	no	—
51	C₂×M₁₆	—	398	2	no	—
52	C₂²×C₈	C₂×D₁₉₉	1	1	yes	characteristic
53	C₂×C₁₆	Dic₁₉₉	1	2	yes	—
54	C₂×C₁₆	Dic₁₉₉	1	2	yes	—
55	C₂×C₁₆	C₂×D₁₉₉	1	2	yes	—
56	#108	—	398	2	no	—
57	#108	—	199	4	no	—
58	C₂²×C₄	D₇₉₆	1	1	yes	characteristic
59	M₁₆	—	796	2	no	—
60	M₁₆	—	398	4	no	—
61	C₂×C₈	—	796	2	no	—
62	C₂×C₈	C₂×Dic₁₉₉	1	1	yes	characteristic
63	C₂×C₈	C₂×Dic₁₉₉	1	1	yes	characteristic
64	C₂×C₈	D₇₉₆	1	1	yes	characteristic
65	C₂×C₈	Dic₃₉₈	1	1	yes	characteristic
66	C₂×C₈	Dic₃₉₈	1	1	yes	characteristic
67	C₂×C₈	C₂²×D₁₉₉	1	1	yes	characteristic
68	C₁₆	C₂×Dic₁₉₉	1	4	yes	—
69	C₂³	Dic₇₉₆	1	1	yes	characteristic
70	C₂×C₄	C₄⋊Dic₁₉₉	1	1	yes	characteristic
71	C₂×C₄	C₄⋊Dic₁₉₉	1	1	yes	characteristic
72	C₂×C₄	D₁₅₉₂	1	1	yes	characteristic
73	C₂×C₄	D₁₅₉₂	1	1	yes	characteristic
74	C₂×C₄	Dic₇₉₆	1	1	yes	characteristic
75	C₂×C₄	C₂×D₇₉₆	1	1	yes	characteristic
76	C₈	—	796	4	no	—
77	C₈	C₄⋊Dic₁₉₉	1	1	yes	characteristic
78	C₈	C₄⋊Dic₁₉₉	1	1	yes	characteristic
79	C₈	C₂²×Dic₁₉₉	1	1	yes	characteristic
80	C₈	C₂×Dic₃₉₈	1	1	yes	characteristic
81	C₂²	—	2	2	no	—
82	C₂²	#20263889	1	1	yes	characteristic
83	C₂²	#20263889	1	1	yes	characteristic
84	C₂²	C₂×Dic₇₉₆	1	1	yes	characteristic
85	C₄	#20263889	1	1	yes	characteristic
86	C₄	#20263889	1	1	yes	characteristic
87	C₄	C₂×C₄⋊Dic₁₉₉	1	1	yes	characteristic
88	C₄	C₂×D₁₅₉₂	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	2	1	no	—
91	C₂	#27163848	1	2	yes	direct product factor
92	C₂	C₂×#20263889	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₅₉₂
commutator	C₈×C₁₉₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉₉
Fitting	C₂²×C₁₆×C₁₉₉	C₂
socle	C₂²×C₁₉₉	#107
prime radical	C₂³×C₁₉₉	Q₁₆
cosocle	C₂×C₈×C₁₉₉	C₂³
hypercenter	C₂²×C₁₆	D₁₉₉
hypocenter	C₁₉₉	C₂×#368
LCS	G ▷ C₈×C₁₉₉ ▷ C₄×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #27163848	C₂	direct (N × H)
44. C₂×C₁₉₉	#368	semidirect
46. C₁₉₉	C₂×#368	semidirect
91. C₂	#27163848	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#20263891	2
#27163848	2
C₂²×C₁₆×C₁₉₉	2
C₂×#368	199

Subgroups — C2×#27163848 #38770642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27163848 #38770642